Are you afraid of failing to live up to your mom's and sister's expectations? Alabama is a really tough recuritment. I'd be scared to death that my mom and sister were expecting me to be a superstar and go DDD and I would do a terrible job at rush and get cut. It would freak me out to have that much pressure.
I also tended to define myself in opposition to my mom for most of my life, so if my mom had been gung ho on joining a sorority, and in particular gung ho on joing one sorority in particular, there would have been no way that I would have rushed or joined her sorority. It's not that I didn't love my mom, but I didn't want to be just like her or do what she said. Mom was awesome, but she was also sort of pushy and controlling and she always knew what was better for me than I did. Just ask her.
My reaction let my mom run my life almost as much as if I did everything my mom thought I should. I was reacting to her ideas and being oppositional, rather than making decisions for my self. Not all of my mom's ideas were bad, but I would NOT admit that for a long time.
So... set aside your mom and your sister. Pretend that no one in your family has ever been in a sorority. Knowing what you know about the experience does it look like something you'd like to do? If my answer was "Yes, that looks like fun,' then I'd go through rush and pledge elsewhere. I wouldn't be a TriDelt, unless I totally fell in love with the house. You sound like you need a little space between you and sister and your mom to develop your own talents and interests. You can do that in another sorority.
If it doesn't sound good, or if you want to spend more time on sports or something else, I wouldn't do it. Tell your mom and your sister that you love them, and you know that they love being in a sorority, but you want to devote your college time to other things. (And have an idea what those things are.) Your mom deserves a reason that doesn't sound critical of her choices or your sister's choices. Make it about you and use "I" statements -- "Mom, I have to tell you something. I know you love your sorority and I respect that, but I don't want to be in a sorority. I want to spend more time on studies/sports/theater/music/band/whatever. I know I'm disappointing you, but I really don't want to go through recruitment."
If the answer is "I don't know what I want to do" then I would go through recruitment. You can always drop, if you really think it isn't for you. I think this would be a good idea, anyway. You know one group of women who are your mom's age and your sister's friends. You probably should meet more groups before you decide that none of them are people you want to hang with. If you decide to list another sorority first, you don't have to tell your mom. She'll just assume that you didn't match with DDD.